OK, this is deeply techie, but for those of us who did DSP at university, and anyone who works in digital signals, the Fast Fourier Transform is no longer the fastest. (It looks from Wikipedia as if it hasn’t been for a while, but the advancements came after I graduated. When I studied this somewhere between 1995 and 1997 the FFT was king.)
The stuff we do in digital radio would really benefit from this kind of stuff because the amount of non-zero Fourier coefficients we are interested in are generally small. Many of the amateur radio modes have just one carrier signal which either changes frequency or changes phase to encode the information. More advanced modes such as Digital Radio Mondiale follow the same kind of pattern, but with more carriers effectively running in parallel. If noise is not a problem with this system then the new algorithm should offer a huge improvement, especially if it can be implemented easily in embedded systems.
The new algorithm is mentioned at http://arxiv.org/abs/1201.2501v1